fix: unwriteable was still can_write in all but name

[ilan-gold]

When I made the change, I just ctrl + F'ed this, but forgot that we inverted the semantics from can_write. We also were never checking the index, which I discovered in #2379

• Closes #
• Tests added

• Release note not necessary because: Unreleased feature fix

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 85.50%. Comparing base (70fcdce) to head (468b2a0).
✅ All tests successful. No failed tests found.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2418      +/-   ##
==========================================
- Coverage   87.44%   85.50%   -1.95%     
==========================================
  Files          49       49              
  Lines        7736     7739       +3     
==========================================
- Hits         6765     6617     -148     
- Misses        971     1122     +151     

Files with missing lines	Coverage Δ
src/anndata/_core/anndata.py	86.49% <100.00%> (+0.05%)	⬆️

... and 8 files with indirect coverage changes

[flying-sheep]

Looks great. Sorry for not catching the missing logic inversion in the original PR.